Snaring a record-setting Tuesday gross, Sony's ''The Amazing Spider-Man'' earned $35 million during its opening day, beating the midweek day's previous record of $27.9 million set by ''Transformers'' over the Fourth of July weekend 2007. Imax boosted Spidey's opening day total by contributing $4 million. "Transformers" grossed a whopping $155 million in its first six days, though that included $8.8 million from evening and late-night screenings on Monday. "Spider-Man," which earned $7.5 million from midnights (added to opening day totals), should see similar traction over the long holiday frame, collecting north of $150 million. That's improved from Sony's earlier estimates in the $110 million-$120 million range. ''Spider-Man'' should do OK business today as an all-audience alternative; Independence Day typically isn't a great moviegoing day for adult fare, which will effect pics like ''Ted'' and ''Magic Mike.'' Overseas, ''Spider-Man'' expands this weekend to markets like Australia, where school holidays start, and throughout most of Europe, as auds there are no longer distracted by the Euro Cup soccer tourney.